Finite groups have more conjugacy classes

We prove that for every $\epsilon > 0$ there exists a $\delta > 0$ so that every group of order $n \geq 3$ has at least $\delta \log_{2} n/{(\log_{2} \log_{2} n)}^{3+\epsilon}$ conjugacy classes. This sharpens earlier results of Pyber and Keller. Bertram speculates whether it is true that every finite group of order $n$ has more than $\log_{3}n$ conjugacy classes. We answer Bertram's question in the affirmative for groups with a trivial solvable radical

Properties of multilayer filters Interim report, 1 Sep. 1969 - 28 Feb. 1970

Using films of gold and silver for optical filter

Properties of multilayer filters Interim report, 1 Mar. - 31 Aug. 1969

Blocking filter effects on long-wavelength rejection of ultraviolet bandpass filte

Properties of multilayer filters Final report, 1 Mar. 1964 - 28 Feb. 1967

Optical interference bandpass filters for ultraviolet spectral regio

Properties of Multilayer Filters Interim Report, 1 Sep. 1965 - 28 Feb. 1966

Circuitry and calibration of solenoid actuated shutter for rapid firing of aluminum and design of ultraviolet band pass filte

Labour Market and Social Policy in Italy: Challenges and Changes. Bertelsmann Policy Brief #2016/02

vEight years after the outbreak of the financial crisis, Italy has still to cope with and overcome a plethora of economic and social challenges. On top of this, it faces an unfavourable demographic structure and severe disparities between its northern and southern regions. Some promising reforms have recently been enacted, specifically targeting poverty and social exclusion. However, much more remains to be done on the way towards greater economic stability and widely shared prosperity

Grating-coupled excitation of multiple surface plasmon-polariton waves

The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are narrower than those representing p-polarized SPP waves. Two incident plane waves propagating in different directions may excite the same SPP wave. A line source could excite several SPP waves simultaneously

Automatic Optimizations for Stream-based Monitoring Languages

Runtime monitors that are specified in a stream-based monitoring language tend to be easier to understand, maintain, and reuse than those written in a standard programming language. Because of their formal semantics, such specification languages are also a natural choice for safety-critical applications. Unlike for standard programming languages, there is, however, so far very little support for automatic code optimization. In this paper, we present the first collection of code transformations for the stream-based monitoring language RTLola. We show that classic compiler optimizations, such as Sparse Conditional Constant Propagation and Common Subexpression Elimination, can be adapted to monitoring specifications. We also develop new transformations -- Pacing Type Refinement and Filter Refinement -- which exploit the specific modular structure of RTLola as well as the implementation freedom afforded by a declarative specification language. We demonstrate the significant impact of the code transformations on benchmarks from the monitoring of unmanned aircraft systems (UAS).Comment: 20th International Conference on Runtime Verification (2020